Recommendation ITU-R BT.601-7(03/2011)

Studio encoding parameters of digital television for standard 4:3 and wide-screen 16:9 aspect ratios

BT SeriesBroadcasting service

(television)

ii Rec. ITU-R BT.601-7

Foreword

The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-frequency spectrum by all radiocommunication services, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted.

The regulatory and policy functions of the Radiocommunication Sector are performed by World and Regional Radiocommunication Conferences and Radiocommunication Assemblies supported by Study Groups.

Policy on Intellectual Property Right (IPR)

ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. Forms to be used for the submission of patent statements and licensing declarations by patent holders are available from http://www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found.

Series of ITU-R Recommendations (Also available online at http://www.itu.int/publ/R-REC/en)

Series Title

BO Satellite deliveryBR Recording for production, archival and play-out; film for televisionBS Broadcasting service (sound)BT Broadcasting service (television)F Fixed serviceM Mobile, radiodetermination, amateur and related satellite servicesP Radiowave propagationRA Radio astronomyRS Remote sensing systemsS Fixed-satellite serviceSA Space applications and meteorologySF Frequency sharing and coordination between fixed-satellite and fixed service systemsSM Spectrum managementSNG Satellite news gatheringTF Time signals and frequency standards emissionsV Vocabulary and related subjects

Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1.

Electronic PublicationGeneva, 2017

ITU 2017

All rights reserved. No part of this publication may be reproduced, by any means whatsoever, without written permission of ITU.

Rec. ITU-R BT.601-7 1

RECOMMENDATION ITU-R BT.601-7*

Studio encoding parameters of digital television for standard 4:3 and wide-screen 16:9 aspect ratios1

(Question ITU-R 1/6)

(1982-1986-1990-1992-1994-1995-2007-2011-2015)

Scope

This Recommendation also covers the pixel characteristics that represent a 525- or 625-line interlace digital television image.

This Recommendation specifies methods for digitally coding video signals. It includes a 13.5 MHz sampling rate for both 4:3 and 16:9 aspect ratio images with performance adequate for present transmission systems.

Keywords

SDTV, digital television image, digital coding, colour difference

The ITU Radiocommunication Assembly,

considering

a) that there are clear advantages for television broadcasters and programme producers in digital studio standards which have the greatest number of significant parameter values common to 525-line and 625-line systems;

b) that a worldwide compatible digital approach will permit the development of equipment with many common features, permit operating economies and facilitate the international exchange of programmes;

c) that an extensible family of compatible digital coding standards is desirable. Members of such a family could correspond to different quality levels, different aspect ratios, facilitate additional processing required by present production techniques, and cater for future needs;

d) that a system based on the coding of components is able to meet these desirable objectives;

e) that the co-siting of samples representing luminance and colour-difference signals (or, if used, the red, green and blue signals) facilitates the processing of digital component signals, required by present production techniques,

recommends

that the following be used as a basis for digital coding standards for television studios in countries using the 525-line system as well as in those using the 625-line system.

1 Extensible family of compatible digital coding standards

1.1 The digital coding should allow the establishment and evolution of an extensible family of compatible digital coding standards. It should be possible to interface simply between any members of the family.

* Radiocommunication Study Group 6 made editorial amendments to this Recommendation in November 2014 and in March 2017 in accordance with Resolution ITU-R 1.

1 Standard definition television (SDTV).

2 Rec. ITU-R BT.601-7

1.2 The digital coding should be based on the use of one luminance and two colour-difference signals (or, if used, the red, green and blue signals).

1.3 The spectral characteristics of the signals must be controlled to avoid aliasing whilst preserving the passband response. Filter specifications are shown in Appendix 2.

2 Specifications applicable to any member of the family

2.1 Sampling structures should be spatially static. This is the case, for example, for the orthogonal sampling structures specified in this Recommendation.

2.2 If the samples represent luminance and two simultaneous colour-difference signals, each pair of colour-difference samples should be spatially co-sited. If samples representing red, green and blue signals are used they should be co-sited.

2.3 The digital standard adopted for each member of the family should permit worldwide acceptance and application in operation; one condition to achieve this goal is that, for each member of the family, the number of samples per line specified for 525-line and 625-line systems shall be compatible (preferably the same number of samples per line).

2.4 In applications of these specifications, the contents of digital words are expressed in both decimal and hexadecimal forms, denoted by the suffixes “d” and “h” respectively.

To avoid confusion between 8-bit and 10-bit representations, the eight most-significant bits are considered to be an integer part while the two additional bits, if present, are considered to be fractional parts.

For example, the bit pattern 10010001 would be expressed as 145d or 91h, whereas the pattern 1001000101 would be expressed as 145.25d or 91.4h.

Where no fractional part is shown, it should be assumed to have the binary value 00.

2.5 Definition of the digital signals Y, CR, CB, from the primary (analogue) signals  ,   and

This paragraph describes, with a view to defining the signals Y, CR, CB, the rules for construction of these signals from the gamma pre-corrected primary analogue signals  ,   and  . The signals are constructed by following the three stages described in § 2.5.1, 2.5.2 and 2.5.3. The method is given as an example, and in practice other methods of construction from these primary signals or other analogue or digital signals may produce identical results. An example is given in § 2.5.4.

2.5.1 Construction of luminance ( ) and colour-difference ( –  ) and ( –  ) signals

The construction of luminance and colour-difference signals is as follows:

then:

( ER' −EY

' )=ER' −0 .299 ER

' − 0. 587 EG' −0 .114 EB

' =0 .701 ER' −0.587 EG

' −0 .114 EB'

and

( EB' −EY

' )=EB' −0 .299 ER

' −0 .587 EG' − 0. 114 EB

' =−0 .299 ER' −0. 587 EG

' +0.886 EB'

Taking the signal values as normalized to unity (e.g. 1.0 V maximum levels), the values obtained for white, black and the saturated primary and complementary colours are shown in Table 1.

Rec. ITU-R BT.601-7 3

TABLE 1

Normalized signal values

Condition –  –

WhiteBlack

1.00

1.00

1.00

1.00

00

00

RedGreenBlue

1.000

01.00

001.0

0.2990.5870.114

– 0.701– 0.587– 0.114

– 0.299– 0.5870.886

YellowCyanMagenta

1.001.0

1.01.00

01.01.0

0.8860.7010.413

0.114– 0.7010.587

– 0.8860.2990.587

2.5.2 Construction of re-normalized colour-difference signals and

Whilst the values for have a range of 1.0 to 0, those for ( –  ) have a range of  0.701 to −0.701 and for ( –  ) a range of  0.886 to −0.886. To restore the signal excursion of the colour-difference signals to unity (i.e.  0.5 to −0.5), re-normalized red and blue colour-difference signals E′CR and E′CB respectively can be calculated as follows:

402.1114.0587.0701.0

402.1BGR

YRC

EEE

EEER

and

ECB

' =EB

' −EY'

1. 772=−0.299 { ER

' −0 . 587 { EG' +0 .886 { EB

'

1 .772¿ ¿¿

The symbols E′CR and E′CB will be used only to designate re-normalized colour-difference signals, i.e. having the same nominal peak-to-peak amplitude as the luminance signal thus selected as the reference amplitude.

2.5.3 Quantization

In the case of a uniformly-quantized 8-bit or 10-bit binary encoding, 28 or 210, i.e. 256 or 1 024, equally spaced quantization levels are specified, so that the range of the binary numbers available is from 0000 0000 to 1111 1111 (00 to FF in hexadecimal notation) or 0000 0000 00 to 1111 1111 11 (00.0h to FF.Ch in hexadecimal notation), the equivalent decimal numbers being 0.00d to 255.75d, inclusive.

In this Recommendation, levels 0.00d and 255.75d are reserved for synchronization data, while levels 1.00d to 254.75d are available for video.

Given that the luminance signal is to occupy only 220 (8-bit) or 877 (10-bit) levels, to provide working margins, and that black is to be at level 16.00d, the decimal value of the quantized luminance signal, Y, is:

Y=int {(219 { E¿¿'Y+16 ) ×D }/D

4 Rec. ITU-R BT.601-7

where D takes either the value 1 or 4, corresponding to 8-bit and 10-bit quantization respectively. The operator int( ) returns the value of 0 for fractional parts in the range of 0 to 0.4999 … and +1 for fractional parts in the range 0.5 to 0.999 ..., i.e. it rounds up fractions above 0.5.

Similarly, given that the colour-difference signals are to occupy 225 (8-bit) or 897 (10-bit) levels and that the zero level is to be level 128.00d, the decimal values of the quantized colour-difference signals, CR and CB, are:

CR= int {(224 { E¿¿ 'C R+128 ) ×D }/D

and

CB=int {(224 { E¿¿ 'CB+128) ×D }/ D

The digital equivalents are termed Y, CR and CB.

2.5.4 Construction of Y, CR , CB via quantization of   ,   ,

In the case where the components are derived directly from the gamma pre-corrected component signals  ,  ,  , or directly generated in digital form, then the quantization and encoding shall be equivalent to:

ERD

' ( in digital form )=int { (219 { E¿¿ 'R +16 )×D }/D

EG D

' ( in digital form )=int {( 219 { E¿¿ 'G +16 )×D }/ D

EBD

' ( in digital form )=int {(219 { E¿¿ 'B +16 )×D }/ D

Then:

Y= int {(0 . 299 { E¿¿ 'RD+0. 587 { E¿¿ ' G D

+0 . 114 { EB D

'¿)¿ D }/D

¿ int {( kY 1'

2m ERD

' +kY 2

'

2m EGD

' +k Y 3

'

2m EBD

' )¿D}/ D

CR=int [{(0.701 { ERD

' −0 .587 { EGD

' −0 .114 {EB D

'¿

¿1 . 402¿) 224

219 +128}×D ] /D¿ int [{( kCR 1

'

2m ERD

' +kCR 2

'

2m EG D

' +kCR 3

'

2m EB D

' )+128}×D ] / D

CB= int [{(−0 .299 { ERD

' −0 .587 { EGD

' +0 . 886 { EBD

'¿

¿1 .772 ¿)224

219 +128}×D ] / D

Rec. ITU-R BT.601-7 5

¿ int [{( k 'CB 1

2m ER D

' +kCB2

'

2m EGD

' +kCB 3

'

2m EBD

' )+128}×D ] /Dwhere k′ and m denote the integer coefficients and the bit-lengths of the integer coefficients, respectively. The integer coefficients of luminance and colour-difference equations should be derived as per Annex 2.

TABLE 2

Integer coefficients of luminance and colour-difference equations

Coefficient bits

Denomi-nator Luminance Y Colour-difference CR Colour-difference CB

m 2m k´Y1 k´Y2 k´Y3 k´CR1 k´CR2 k´CR3 k´CB1 k´CB2 k´CB3

8 256 77 150 29 131 −110 −21 −44 −87 1319 512 153 301 58 262 −219 −43 −88 −174 26210 1 024 306 601 117 524 −439 −85 −177 −347 52411 2 048 612 1 202 234 1 047 −877 −170 −353 −694 1 04712 4 096 1 225 2 404 467 2 095 −1 754 −341 −707 −1 388 2 09513 8 192 2 449 4 809 934 4 189 −3 508 −681 −1 414 −2 776 4 190

14 16 384 4 899 9 617 1 868 8 379 −7 016 −1 363 −2 828 −5 551 8 379

15 32 768 9 798 19 235 3 735 16 758 −14 033 −2 725 −5 655 −11 10

3 16 758

16 65 536 19 595 38 470 7 471 33 516 −28 066 −5 450 −11 311 −22 20

5 33 516

NOTE 1 – The bold values indicate that the values are modified from the nearest integer values by the optimization.

To obtain the 4:2:2 components Y, CR, CB, low-pass filtering and sub-sampling must be performed on the 4:4:4 CR, CB signals described above. Note should be taken that slight differences could exist between CR, CB components derived in this way and those derived by analogue filtering prior to sampling.

2.5.5 Limiting of Y, CR , CB signals

Digital coding in the form of Y, CR, CB signals can represent a substantially greater gamut of signal values than can be supported by the corresponding ranges of R, G, B signals. Because of this it is possible, as a result of electronic picture generation or signal processing, to produce Y, CR, CB

signals which, although valid individually, would result in out-of-range values when converted to R, G, B. It is both more convenient and more effective to prevent this by applying limiting to the Y, CR, CB signals than to wait until the signals are in R, G, B form. Also, limiting can be applied in a way that maintains the luminance and hue values, minimizing the subjective impairment by sacrificing only saturation.

6 Rec. ITU-R BT.601-7

2.6 Colour and opto-electronic transfer characteristic2

ItemCharacteristics

Parameter 625 525

2.6.1 Chromaticity coordinates, CIE 1931(1) x y x yPrimaries Red 0.640 0.330 0.630 0.340

Green 0.290 0.600 0.310 0.595Blue 0.150 0.060 0.155 0.070

2.6.2 Assumed chromaticity for equal primary signals – Reference white

D65

x yER EG EB 0.3127 0.3290

2.6.3 Opto-electronic transfer characteristics before non-linear precorrection

Assumed linear

2.6.4 Overall opto-electronic transfer characteristic at source3

E (1.099 L0.45 – 0.099) for 1.00 L 0.018E 4.500 L for 0.018 L 0where:L: luminance of the image 0 L 1 for conventional colorimetryE: corresponding electrical signal.

(1) Chromaticity coordinates specified are those currently used by 625-line and 525-line conventional systems.

3 Family members

The following family members are defined:– 4:2:2 for 4:3 aspect ratio, and for wide-screen 16:9 aspect ratio systems when it is necessary

to keep the same analogue signal bandwidth and digital rates for both aspect ratios.– 4:4:44 for 4:3 and 16:9 aspect ratio systems with higher colour resolution.

2 It is recognized that a practice is now sometimes used by which, when programs produced in HDTV are release in SDTV, their HDTV pixel map is re-mapped onto the SDTV pixel map without changing the colorimetry of the original program.

3 In typical production practice the encoding function of image sources is adjusted so that the final picture has the desired look, as viewed on a reference monitor having the reference decoding function of Rec. ITU-R BT.1886, in the reference viewing environment defined in Rec. ITU-R BT.2035. Although some parameters listed in Recommendation ITU-R BT.2035 are intended for HDTV signal viewing, scaled viewing distances for SDTV signals should be used.

4 In the 4:4:4 members of the family the sampled signals may be luminance and colour difference signals (or, if used, red, green and blue signals).

Rec. ITU-R BT.601-7 7

Annex 1

Encoding parameters for members of the family

1 Encoding parameter values for the 4:2:2 member of the family

The specification (see Table 3) applies to the 4:2:2 member of the family, to be used for the standard digital interface between main digital studio equipment and for international programme exchange of 4:3 aspect ratio digital television or wide-screen 16:9 aspect ratio digital television when it is necessary to keep the same analogue signal bandwidth and digital rates.

TABLE 3

Parameters 525-line, 60/1.001, field/ssystems

625-line, 50 field/ssystems

1) Coded signals: Y, CR, CB These signals are obtained from gamma pre-corrected signals, namely: ,  –  ,  –  (see § 2.5)

2) Number of samples per total line:– luminance signal (Y)– each colour-difference

signal (CR, CB)

858429

864432

3) Sampling structure Orthogonal, line, field and frame repetitive. CR and CB samples co-sited with odd (1st, 3rd, 5th, etc.) Y samples in each line

4) Sampling frequency:

– luminance signal– each colour-difference

signal

13.5 MHz6.75 MHz

The tolerance for the sampling frequencies should coincide with the tolerance for the line frequency of the relevant colour television standard

5) Form of coding Uniformly quantized PCM, 8 or 10 bits per sample, for the luminance signal and each colour-difference signal

6) Number of samples per digital active line:– luminance signal– each colour-difference

signal

720360

7) Analogue-to-digital horizontal timing relationship:– from end of digital active

line to OH

16 luminance clock periods 12 luminance clock periods

8 Rec. ITU-R BT.601-7

TABLE 3 (end)

Parameters 525-line, 60/1.001, field/ssystems

625-line, 50 field/ssystems

8) Correspondence between video signal levels and quantization levels:– scale– luminance signal– each colour-difference

signal

(See § 2.4) (Values are decimal)

0.00d to 255.75d

220 (8-bit) or 877 (10-bit) quantization levels with the black level corresponding to level 16.00d and the peak white level corresponding to level 235.00d. The signal level may occasionally excurse beyond level 235.00d or below level 16.00d.225 (8-bit) or 897 (10-bit) quantization levels in the centre part of the quantization scale with zero signal corresponding to level 128.00d. The signal level may occasionally excurse beyond level 240.00d or below level 16.00d.

9) Code-word usage Code words corresponding to quantization levels 0.00d and 255.75d

are used exclusively for synchronization. Levels 1.00d to 254.75d are available for video. When 8-bit words are treated in 10-bit system, two LSBs of zeros are to be appended to the 8-bit words.

2 Encoding parameter values for the 4:4:4 member of the family

The specifications given in Table 4 apply to the 4:4:4 member of the family suitable for television source equipment and high-quality video signal processing applications.

TABLE 4

Parameters 525-line, 60/1.001 field/ssystems

625-line, 50 field/ssystems

1) Coded signals: Y, CR, CB or R, G, B

These signals are obtained from gamma pre-corrected signals, namely: ,  –  ,  –  or , ,

2) Number of samples per total line for each signal 858 864

3. Sampling structure Orthogonal, line, field and frame repetitive. The three sampling structures to be coincident and coincident also with the luminance sampling structure of the 4:2:2 member

4) Sampling frequency for each signal

13.5 MHz

5) Form of coding Uniformly quantized PCM, 8 or 10 bits per sample6) Duration of the digital active

line expressed in number of samples

720

7) Analogue-to-digital horizontal timing relationship:

– from end of digital active line to OH

16 clock periods 12 clock periods

Rec. ITU-R BT.601-7 9

TABLE 4 (end)

Parameters 525-line, 60/1.001 field/ssystems

625-line, 50 field/ssystems

8) Correspondence between video signal levels and quantization level for each sample:– scale– R, G, B or luminance

signal(1)

– each colour-difference signal(1)

(See § 2.4) (Values are decimal)

0.00d to 255.75d220 (8-bit) or 877 (10-bit) quantization levels with the black level corresponding to level 16.00d and the peak white level corresponding to level 235.00d. The signal level may occasionally excurse beyond level 235.00d or below level 16.00d.225 (8-bit) or 897 (10-bit) quantization levels in the centre part of the quantization scale with zero signal corresponding to level 128.00d. The signal level may occasionally excurse beyond level 240.00d or below level 16.00d.

9) Code-word usage Code words corresponding to quantization levels 0.00d and 255.75d

are used exclusively for synchronization. Levels 1.00d to 254.75d are available for video.When 8-bit words are treated in 10-bit system, two LSBs of zeros are to be appended to the 8-bit words.

(1) If used.

Appendix 1to Annex 1

Definition of signals used in the digital coding standards

1 Relationship of digital active line to analogue sync reference

The relationship between the digital active line luminance samples and the analogue synchronizing reference is shown in:– Figure 1 for 625-line.– Figure 2 for 525-line.

In the Figures, the sampling point occurs at the commencement of each block.

The respective numbers of colour-difference samples in the 4:2:2 family can be obtained by dividing the number of luminance samples by two. The (12,132), and (16,122) were chosen symmetrically to dispose the digital active line about the permitted variations. They do not form part of the digital line specification and relate only to the analogue interface.

10 Rec. ITU-R BT.601-7

FIGURE 1

FIGURE 2

Rec. ITU-R BT.601-7 11

Appendix 2to Annex 1

Filtering characteristics

1 Some guidance on the practical implementation of the filters

In the proposals for the filters used in the encoding and decoding processes, it has been assumed that, in the post-filters which follow digital-to-analogue conversion, correction for the (sin x/x) characteristic is provided. The passband tolerances of the filter plus (sin x/x) corrector plus the theoretical (sin x/x) characteristic should be the same as given for the filters alone. This is most easily achieved if, in the design process, the filter, (sin x/x) corrector and delay equalizer are treated as a single unit.

The total delays due to filtering and encoding the luminance and colour-difference components should be the same. The delay in the colour-difference filter (Figs 4a) and 4b)) is typically double that of the luminance filter (Figs 3a) and 3b)). As it is difficult to equalize these delays using analogue delay networks without exceeding the passband tolerances, it is recommended that the bulk of the delay differences (in integral multiples of the sampling period) should be equalized in the digital domain. In correcting for any remainder, it should be noted that the sample-and-hold circuit in the decoder introduces a flat delay of one half a sampling period.

The passband tolerances for amplitude ripple and group delay are recognized to be very tight. Present studies indicate that it is necessary so that a significant number of coding and decoding operations in cascade may be carried out without sacrifice of the potentially high quality of the 4:2:2 coding standard. Due to limitations in the performance of currently available measuring equipment, manufacturers may have difficulty in economically verifying compliance with the tolerances of individual filters on a production basis. Nevertheless, it is possible to design filters so that the specified characteristics are met in practice, and manufacturers are required to make every effort in the production environment to align each filter to meet the given templates.

The specifications given in Appendix 2 were devised to preserve as far as possible the spectral content of the Y, CR, CB signals throughout the component signal chain. It is recognized, however, that the colour-difference spectral characteristic must be shaped by a slow roll-off filter inserted at picture monitors, or at the end of the component signal chain.

12 Rec. ITU-R BT.601-7

FIGURE 3Filter template for a luminance, RGB or 4:4:4 colour-difference signal

Rec. ITU-R BT.601-7 13

FIGURE 4Filter template for a 4:2:2 colour-difference signal

14 Rec. ITU-R BT.601-7

FIGURE 5Digital filter template for sampling-rate conversion

from 4:4:4 to 4:2:2 colour difference signals

Rec. ITU-R BT.601-7 15

Annex 2

Derivation of integer coefficients of luminance and colour-difference equations for the conventional colour gamut system

Digital systems may introduce computation errors in the luminance and colour-difference signals due to the finite bit-length of the equation coefficients. Also, digital luminance and colour-difference signals may take slightly different values depending on the signal processing sequence, i.e. the discrepancy between signals quantized after analogue matrixing and signals digitally matrixed after quantization of RGB signals. To minimize such errors and discrepancies, the integer coefficients for the digital equations should be optimized. The optimization procedure and the resultant integer coefficients for several bit-lengths are given in the following.

1 Digital equations

In the following, m and n denote the bit-lengths of the integer coefficients and digital signals, respectively.

The digital luminance equation for the conventional colour gamut system is described as follows:

DY' =INT [ 0. 299 DR

' +0.587 DG' +0 . 114 DB

' ] (1)

=INT [ rY 1'

2m DR' +

rY 2'

2m DG' +

rY 3'

2m DB' ] (2)

¿ INT [ k Y 1'

2m DR' +

kY 2'

2m DG' +

kY 3'

2m DB' ] (3)

where r' and k' denote the real values of the coefficient and the integer coefficients, respectively, given below:

rY 1' =0. 299 × 2m kY 1

' =INT [rY 1' ]

rY 2' =0. 587 × 2m kY 2

' =INT [rY 2' ]

rY 3' =0 .114 × 2m kY 3

' =INT [rY 3' ]

The digital colour-difference equations for the conventional colour gamut system are described as follows:

DCB' =INT [−0 .299 DR

' −0 . 587 DG' +0 . 886 DB

'

1 .772× 224

219+2n−1] (4)

=INT [ r CB 1'

2m DR' +

rCB 2'

2m DG' +

rCB 3'

2m DB' +2n−1 ] (5)

16 Rec. ITU-R BT.601-7

¿ INT [ kCB 1'

2m DR' +

kCB 2'

2m DG' +

kCB 3'

2m DB' +2n−1] (6)

DCR' = INT [ 0 .701 DR

' −0 . 587 DG' −0 . 114 DB

'

1 . 402× 224

219+2n−1 ] (7)

=INT [ r CR 1'

2m DR' +

r CR 2'

2m DG' +

rCR3'

2m DB' +2n−1] (8)

¿ INT [ kCR 1'

2m DR' +

kCR 2'

2m DG' +

kCR 3'

2m DB' +2n−1] (9)

where:

rCB 1' =−0 .299

1 .772× 224

219× 2m

kCB 1' =INT [ rCB 1

' ]

rCB 2' =−0 .587

1 .772× 224

219× 2m

kCB 2' =INT [ rCB 2

' ]

rCB3' =0 .886

1 .772× 224

219× 2m

kCB 3' =INT [ rCB 3

' ]

rCR 1' =0 .701

1.402× 224

219× 2m

kCR 1' =INT [ rCR 1

' ]

rCR 2' =−0 .587

1 . 402× 224

219× 2m

kCR 2' =INT [ rCR 2

' ]

rCR 3' =−0 .114

1. 402× 224

219× 2m

kCR 3' =INT [rCR 3

' ]

2 Optimization procedure

Equation (3) shows the digitally matrixed luminance signal which includes computation errors due to the finite bit-length of the integer coefficients. When the coefficient bit-length is increased, the argument (the value in [ ]) of equation (3) gets close to that of equation (2), resulting in the reduced errors or discrepancies between the equations. Therefore, the difference between the arguments of equations (2) and (3) can be regarded as a measure of the integer coefficient optimization. As the difference of arguments depends on input RGB signals, “Least Square Error” optimization is defined, in which the integer coefficients are adjusted in such a way that the sum of the squared difference over all inputs falls into the minimum value, that is, the value of equation (10) is minimized.

ε Y' = ∑

for all RGB {( kY 1'

2m DR' +

k Y 2'

2m DG' +

kY 3'

2m DB' )−( rY 1

'

2m DR' +

rY 2'

2m DG' +

rY 3'

2m DB' )}

2

(10)

Rec. ITU-R BT.601-7 17

In addition to providing the minimum r.m.s. errors, this LSE optimization automatically minimizes the peak error that takes place at a particular input colour (a particular combination of input RGB signals), as well as the discrepancy between different signal processing sequences (analogue-matrixing and digital-matrixing).

The optimization procedure is as follows:

Step 1: For the initial value of each integer coefficient rYj'

(j 1, 2, 3), take the nearest integer to the real value of the coefficient rYj

'.

Step 2: With the initial integer coefficients, calculate the r.m.s. errors or the squared difference sum (equation (10)) over the input RGB signal range, e.g., 16 through 235 for an 8-bit system (a simple calculation method without using summation is described in § 3).

Step 3: Examine the r.m.s. errors when increasing/decreasing each integer coefficient by one. 27 (  33) combinations must be evaluated in total, because each coefficient can take three values, i.e. increased, decreased and unchanged from the initial value.

Step 4: Select the combination of the coefficients that gives the minimum r.m.s. error. This combination is the resultant optimized one.

The same procedure is applied for the colour-difference equations, using equations (11) and (12).

ε CB' = ∑

for all RGB {( kCB 1'

2m DR' +

k CB 2'

2m DG' +

kCB3'

2m DB' +2n−1)

−( rCB 1'

2m DR' +

rCB 2'

2m DG' +

r CB 3'

2m DB' +2n−1)}

2

(11)

ε CR' = ∑

for all RGB {( k CR 1'

2m DR' +

kCR 2'

2m DG' +

kCR 3'

2m DB' +2n−1)

−( rCR 1'

2m DR' +

rCR 2'

2m DG' +

rCR3'

2m DB' +2n−1)}

2

(12)

3 Simple calculation method for squared difference sum

By expressing the difference between integer and real coefficients value as ij  k'ij – r'ij, and the digital RGB signals as Xj, the sum of the squared differences of equations (10) to (12) can be written as the following:

ε i'= 1

2m ∑X 1=L

H

∑X2=L

H

∑X 3=L

H

(δ i1 X1+δi 2 X2+δi3 X3)2

(13)

where L and H denote the lower and upper boundaries of the input signal range, respectively, for which the integer coefficients are to be optimized.

As L and H are constant in the digital system under consideration, the summations for Xj are also constant. Then equation (13) can be expressed as a function only of ij.

18 Rec. ITU-R BT.601-7

ε i' = 1

2m { N1 (δi 12 +δ i2

2 +δi 32 ) + 2 N2 ( δi 1δi 2 +δi2 δi 3 +δi3 δi 1 )}

(14)

where:

N1=∑X2=L

H

∑X 3=L

H

( ∑X1=L

H

X12)= ∑

X 1=L

H

∑X3=L

H

( ∑X 2=L

H

X12)= ∑

X 1=L

H

∑X 2=L

H

( ∑X 3=L

H

X12)

=( H−L+1 )2 {H ( H +1 ) (2H +1 )/6−( L−1) L(2 L−1)/6}

N2=∑X3=L

H

( ∑X 1=L

H

∑X2= L

H

X1 X 2)=∑X 1= L

H

(∑X2= L

H

∑X 3=L

H

X2 X3)=∑X2= L

H

( ∑X3=L

H

∑X 1=L

H

X3 X 1)=( H−L+1 ) {H ( H +1)/2−( L−1) L/2}2

Thus the calculation of r.m.s. errors or equations (10) to (12) can be simply performed by equation (14).

______________